Theorem orim2d 777

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 775	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 697

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  orim2  778  orbi2d  779  pm2.82  801  stdcndcOLD  831  pm2.13dc  870  exmid1dc  4123  acexmidlemcase  5769  poxp  6129  fodjuomnilemdc  7016  indpi  7150  suplocexprlemloc  7529  nneoor  9153  uzp1  9359  maxabslemlub  10979  xrmaxiflemlub  11017  exmidunben  11939  bj-nn0suc  13162  sbthomlem  13220